Brian White
Robert Grimmett Professor of Mathematics
Academic Appointments

Professor, Mathematics
Administrative Appointments

National Science Foundation Postdoctoral Research Fellow, Courant Institute (1981  1983)

Assistant Professor, Stanford University (1983  1985)

Associate Professor, Stanford University (1985  1992)

Professor, Stanford University (1992  Present)
Honors & Awards

7th highest score on Putnam Mathematics Competition (open to all US and Canadian undergraduates), The Mathematical Association of America (1975)

Highest ranking Yale senior in sciences, Yale University (1977)

Graduate Fellowship, National Science Foundation (1977)

Postdoctoral Fellowship, National Science Foundation (19811983)

Alfred P. Sloan Fellowship, Alfred P. Sloan Foundation (19851986)

Presidential Young Investigator Award, National Science Foundation (19861991)

Bing Teaching Award, Stanford University (1993)

Guggenheim Fellowship, Guggenheim Foundation (1999)
Boards, Advisory Committees, Professional Organizations

Member, National Science Foundation (1983  Present)

Director of undergraduate studies, Mathematics Department, Stanford University (2005)

Math and Computational Sciences advisory board member, Stanford University
Professional Education

Ph.D., Princeton University (1982)

M.S., Princeton University (1981)

B.S./M.S., Yale University (1977)
202021 Courses
 Fundamental Concepts of Analysis
MATH 171 (Sum)  Proofs and Modern Mathematics
MATH 56 (Win) 
Independent Studies (2)
 Advanced Reading and Research
MATH 360 (Aut, Win, Spr, Sum)  Reading Topics
MATH 199 (Spr)
 Advanced Reading and Research

Prior Year Courses
201920 Courses
 Linear Algebra, Multivariable Calculus, and Modern Applications
MATH 51 (Aut)  Topics in Differential Geometry
MATH 286 (Spr)
201819 Courses
 Modern Mathematics: Continuous Methods
MATH 63CM (Spr)  Real Analysis
MATH 205A (Aut)
201718 Courses
 Graduate Teaching Seminar
MATH 355 (Spr)  Linear Algebra and Differential Calculus of Several Variables
MATH 51 (Spr)  Real Analysis
MATH 205A (Aut)
 Linear Algebra, Multivariable Calculus, and Modern Applications
All Publications

Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
2020; 73 (3): 558–80
View details for DOI 10.1002/cpa.21852
View details for Web of Science ID 000507507900002

A local regularity theorem for mean curvature flow with triple edges
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
2020; 758: 281–305
View details for DOI 10.1515/crelle20170044
View details for Web of Science ID 000505592100009

Sharp entropy bounds for selfshrinkers in mean curvature flow
GEOMETRY & TOPOLOGY
2019; 23 (3): 1611–19
View details for DOI 10.2140/gt.2019.23.1611
View details for Web of Science ID 000469876000009

On the compactness theorem for embedded minimal surfaces in 3manifolds with locally bounded area and genus
COMMUNICATIONS IN ANALYSIS AND GEOMETRY
2018; 26 (3): 659–78
View details for Web of Science ID 000439729000007

Helicoidal minimal surfaces of prescribed genus
ACTA MATHEMATICA
2016; 216 (2): 217323
View details for DOI 10.1007/s115110160139z
View details for Web of Science ID 000388120500002

Subsequent singularities in meanconvex mean curvature flow
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
2015; 54 (2): 14571468
View details for DOI 10.1007/s0052601508314
View details for Web of Science ID 000361391500010

CURVATURES OF EMBEDDED MINIMAL DISKS BLOW UP ON SUBSETS OF C1 CURVES
JOURNAL OF DIFFERENTIAL GEOMETRY
2015; 100 (2): 389394
View details for Web of Science ID 000355355700005

PROPERLY EMBEDDED, AREAMINIMIZING SURFACES IN HYPERBOLIC 3SPACE
JOURNAL OF DIFFERENTIAL GEOMETRY
2014; 97 (3): 515544
View details for Web of Science ID 000340352800005

THE ROUND SPHERE MINIMIZES ENTROPY AMONG CLOSED SELFSHRINKERS
JOURNAL OF DIFFERENTIAL GEOMETRY
2013; 95 (1): 5369
View details for Web of Science ID 000322654700003

Topological change in mean convex mean curvature flow
INVENTIONES MATHEMATICAE
2013; 191 (3): 501525
View details for DOI 10.1007/s0022201203970
View details for Web of Science ID 000314980600001

Sequences of embedded minimal disks whose curvatures blow up on a prescribed subset of a line
COMMUNICATIONS IN ANALYSIS AND GEOMETRY
2011; 19 (3): 487502
View details for Web of Science ID 000296081800002

AXIAL MINIMAL SURFACES IN S2 x R ARE HELICOIDAL
JOURNAL OF DIFFERENTIAL GEOMETRY
2011; 87 (3): 515523
View details for Web of Science ID 000295439600004

The maximum principle for minimal varieties of arbitrary codimension
COMMUNICATIONS IN ANALYSIS AND GEOMETRY
2010; 18 (3): 421432
View details for Web of Science ID 000285725100001

WHICH AMBIENT SPACES ADMIT ISOPERIMETRIC INEQUALITIES FOR SUBMANIFOLDS?
JOURNAL OF DIFFERENTIAL GEOMETRY
2009; 83 (1): 213228
View details for Web of Science ID 000270193800008

CURRENTS AND FLAT CHAINS ASSOCIATED TO VARIFOLDS, WITH AN APPLICATION TO MEAN CURVATURE FLOW
DUKE MATHEMATICAL JOURNAL
2009; 148 (1): 4162
View details for DOI 10.1215/001270942009019
View details for Web of Science ID 000265672400002

The geometry of genusone helicoids
COMMENTARII MATHEMATICI HELVETICI
2009; 84 (3): 547569
View details for Web of Science ID 000268738900004

Genusone helicoids from a variational point of view
COMMENTARII MATHEMATICI HELVETICI
2008; 83 (4): 767813
View details for Web of Science ID 000261133900004

ON THE NUMBER OF MINIMAL SURFACES WITH A GIVEN BOUNDARY
Conference on Differential Geometry, Mathematical Physics, Mathematics and Society
SOC MATHEMATIQUE FRANCE. 2008: 207–24
View details for Web of Science ID 000272458900008
 A local regularity theorem for mean curvature flow Annals of Mathematics 2005; 161: 1487–1519
 The nature of singularities in mean curvature flow of meanconvex sets Journal of the American Mathematical Society 2003; 16: 123138
 Evolution of curves and surfaces by mean curvature Proceedings of the International Congress of Mathematicians 2002
 Embeddedness of minimal surfaces with total boundary curvature at most 4π Annals of Mathematics 2002; 155: 209–234
 The size of the singular set in mean curvature flow of meanconvex surfaces Journal of the American Mathematical Society 2000; 13: 665695
 The deformation theorem for flat chains Acta Mathematica 1999; 183: 255271
 Rectifiability of flat chains Annals of Mathematics 1999; 150: 165184
 The mathematics of F. J. Almgren, Jr Journal of Geometric Analysis 1998; 8: 681702
 A new proof of Federer’s structure theorem for kdimensional sets in Rⁿ Journal of the American Mathematical Society 1998; 11: 693–701
 Soapfilms bounded by nonclosed curves Journal of Geometric Analysis 1998; 8: 239–250
 Classical area minimizing surfaces with real analytic boundaries Acta Mathematica 1997; 179: 295305
 The mathematics of F. J. Almgren, Jr Notices of the AMS  American Mathematical Society 1997; 44 (10): 14511456
 Stratification of minimal surfaces, mean curvature flows, and harmonic maps Journal fur die Reine und Angewandte Mathematik 1997; 488: 135
 Existence of leastenergy configurations of immiscible fluids Journal of Geometric Analysis 1996; 6: 151–161
 Half of enneper’s surface minimizes area Geometric analysis and the calculus of variations for Stefan Hildebrandt edited by Jost, J. International Press. 1996: 361–368
 The topology of hypersurfaces moving by mean curvature Communications in analysis and geometry 1995; 3: 317–333
 The bridge principle for unstable and for singular minimal surfaces Communications in analysis and geometry 1994; 2: 513532
 Some questions of De Giorgi about mean curvature flow of triply periodic surfaces Motion by Mean Curvature edited by Buttazzo, B., Visintin, A. de Gruyter. 1994: 210–213
 A strong minimax property of nondegenerate minimal submanifolds Journal fur die Reine und Angewandte Mathematik 1994; 457: 203–218
 The structure of branch points in area minimizing surfaces and in pseudoholomorphic curves Annals of Mathematics 1994; 139: 3585
 Partial regularity of meanconvex hypersurfaces flowing by mean curvature International Mathematics Research Notice 1994; 4: 185192
 The bridge principle for stable minimal surfaces Calculus of Variations and Partial Differential Equations 1994; 2: 405425
 The Space of Minimal Annuli Bounded by an Extremal Pair of Planar Curves Communications in Analysis and Geometry 1993; 1: 415437
 On the topological type of minimal submanifolds Topology 1992; 31: 445448
 Nonunique tangent maps at isolated singularities of harmonic maps Bulletin of the American Mathematical Society 1992; 26: 125129
 The space of minimal submanifolds for varying riemannian metrics Indiana University Mathematics Journal 1991; 40: 161200
 Existence of smooth embedded surfaces of prescribed topological type that minimize parametric even elliptic functionals on threemanifolds Journal of Differential Geometry 1991; 33: 413443
 Minimal Surfaces Bounded by Convex Curves in Parallel Planes Commentarii Mathematici Helvetici 1991; 66: 263278
 A rigidity theorem for properly embedded minimal surfaces in R³ Journal of Differential Geometry 1990; 32: 6576
 A strong maximum principle for varifolds that are stationary with respect to even parametric elliptic functionals Indiana University Mathematics Journal 1989; 38: 683–691
 A new proof of the compactness theorem for integral currents Commentarii Mathematici Helvetici 1989; 64: 207–220
 New applications of mapping degrees to minimal surface theory Journal of Differential Geometry 1989; 29: 143162
 Some Recent Developments in Differential Geometry Mathematical Intelligencer 1989; 11: 41–47
 Every threesphere of positive ricci curvature contains a minimal embedded torus Bulletin (New Series) of the American Mathematical Society 1989; 21: 7175
 The rate of convergence of a harmonic map at a singular point Mathematische Annalen 1989; 283: 539549
 Complete surfaces of finite total curvature Journal of Differential Geometry 1988; 28: 359–360
 Homotopy classes in sobolev spaces and the existence of energy minimizing maps Acta Mathematica 1988; 160: 1–17
 Curvature estimates and compactness theorems in 3manifolds for surfaces that are stationary for parametric elliptic functionals Inventiones Mathematicae 1987; 88: 243–256
 The space of mdimensional surfaces that are stationary for a parametric elliptic integrand Indiana University Mathematics Journal 1987; 36: 567–602
 A regularity theorem for minimizing hypersurfaces modulo p Proceedings of Symposia in Pure Mathematics 1986; 44: 413–427
 Infima of energy functionals in homotopy classes of mappings Journal of Differential Geometry 1986; 23: 127–142
 Generic regularity of unoriented twodimensional area minimizing surfaces Annals of Mathematics 1986; 124: 403
 Homotopy classes in sobolev spaces and energy minimizing maps Bulletin of the American Mathematical Society 1985; 13: 166–168
 Regularity of singular sets in immiscible fluid interfaces and in solutions to other plateautype problems Proceedings of the Centre for Mathematical Analysis 1985: 244249
 Mappings that minimize area in their homotopy classes Journal of Differential Geometry 1984; 20: 433–446
 The least area bounded by multiples of a curve Proceedings from the American Mathematical Society 1984; 90: 230–232
 Tangent cones to 2dimensional areaminimizing integral currents are unique Duke Mathematical Journal 1983; 50: 143–160
 Existence of leastarea mappings of Ndimensional domains Annals of Mathematics 1983; 118 : 179–185
 Regularity of areaminimizing hypersurfaces at boundaries with multiplicity Annals of Mathematics Studies 1983 ; 103: 293–301
 The structure of minimizing hypersurfaces mod 4 Inventiones Mathematicae 1979 ; 53: 45–58